January 2 2011 1:10:43.221 PM FEM2D_POISSON_SPARSE FORTRAN90 version: A version of FEM2D_POISSON using sparse storage and an iterative solver. Solution of the Poisson equation in an arbitrary region in 2 dimensions. - DEL H(x,y) DEL U(x,y) + K(x,y) * U(x,y) = F(x,y) in the region U(x,y) = G(x,y) on the boundary. The finite element method is used, with triangular elements, which must be a 3 node linear triangle. Node file is "ell_nodes.txt". Element file is "ell_elements.txt". Number of nodes = 65 First 10 nodes Row 1 2 Col 1 0.00000 0.00000 2 0.00000 0.500000 3 0.500000 0.00000 4 0.00000 1.00000 5 0.500000 0.500000 6 1.00000 0.00000 7 0.00000 1.50000 8 0.500000 1.00000 9 1.00000 0.500000 10 1.50000 0.00000 Element order = 3 Number of elements = 96 First 10 elements Row 1 2 3 Col 1 1 3 2 2 6 5 3 3 4 2 5 4 3 5 2 5 23 22 10 6 21 9 22 7 6 10 9 8 22 9 10 9 19 7 20 10 4 8 7 Quadrature order = 3 Number of nonzero coefficients NZ_NUM = 385 Part of Finite Element matrix A: Col: 1 2 3 4 5 Row --- 1 1.02083 -0.489583 -0.489583 0.00000 0.00000 2 -0.489583 2.06250 0.208333E-01 -0.489583 -0.979167 3 -0.489583 0.208333E-01 2.06250 0.00000 -0.979167 4 0.00000 -0.489583 0.00000 2.06250 0.208333E-01 5 0.00000 -0.979167 -0.979167 0.208333E-01 4.12500 6 0.00000 0.00000 -0.489583 0.00000 0.208333E-01 7 0.00000 0.00000 0.00000 -0.489583 0.00000 8 0.00000 0.00000 0.00000 -0.979167 -0.979167 9 0.00000 0.00000 0.00000 0.00000 -0.979167 Col: 6 7 8 9 10 Row --- 3 -0.489583 0.00000 0.00000 0.00000 0.00000 4 0.00000 -0.489583 -0.979167 0.00000 0.00000 5 0.208333E-01 0.00000 -0.979167 -0.979167 0.00000 6 2.06250 0.00000 0.00000 -0.979167 -0.489583 7 0.00000 2.06250 0.208333E-01 0.00000 0.00000 8 0.00000 0.208333E-01 4.12500 0.208333E-01 0.00000 9 -0.979167 0.00000 0.208333E-01 4.12500 0.208333E-01 10 -0.489583 0.00000 0.00000 0.208333E-01 2.06250 Part of right hand side vector F: 1 -.16406250 2 -.46875000 3 -.46875000 4 -.38541667 5 -.85416667 6 -.38541667 7 -.23958333 8 -.66666667 9 -.66666667 10 -.23958333 Part of A after adjustment for Dirichlet condition: Col: 1 2 3 4 5 Row --- 1 1.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 1.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 1.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 1.00000 0.00000 5 0.00000 -0.979167 -0.979167 0.208333E-01 4.12500 8 0.00000 0.00000 0.00000 -0.979167 -0.979167 9 0.00000 0.00000 0.00000 0.00000 -0.979167 Col: 6 7 8 9 10 Row --- 5 0.208333E-01 0.00000 -0.979167 -0.979167 0.00000 6 1.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 1.00000 0.00000 0.00000 0.00000 8 0.00000 0.208333E-01 4.12500 0.208333E-01 0.00000 9 -0.979167 0.00000 0.208333E-01 4.12500 0.208333E-01 10 0.00000 0.00000 0.00000 0.00000 1.00000 Part of F after adjustment for Dirichlet condition: 1 0.0000000 2 0.25000000 3 0.25000000 4 1.0000000 5 -.85416667 6 1.0000000 7 2.2500000 8 -.66666667 9 -.66666667 10 2.2500000 ITR = 1 Residual = 68.3088 K = 1 Residual = 50.3097 K = 2 Residual = 33.4221 K = 3 Residual = 18.7220 K = 4 Residual = 9.71637 K = 5 Residual = 5.43785 K = 6 Residual = 2.86222 K = 7 Residual = 1.51663 K = 8 Residual = 0.632429 K = 9 Residual = 0.224386 K = 10 Residual = 0.707548E-01 K = 11 Residual = 0.264148E-01 K = 12 Residual = 0.649285E-02 K = 13 Residual = 0.218970E-02 K = 14 Residual = 0.657136E-03 K = 15 Residual = 0.180903E-03 K = 16 Residual = 0.605025E-04 K = 17 Residual = 0.264275E-04 K = 18 Residual = 0.144706E-04 K = 19 Residual = 0.249499E-05 K = 20 Residual = 0.972453E-06 MGMRES: Iterations = 20 Final Residual = 0.972453E-06 Part of the solution vector U: 1 -.17376101E-11 2 0.25000000 3 0.25000000 4 1.0000000 5 0.48493557 6 1.0000000 7 2.2500000 8 1.2289069 9 1.2289068 10 2.2500000 FEM2D_POISSON_SPARSE: Wrote an ASCII file "ell_solution.txt" of the form U ( X(I), Y(I) ) which can be used for plotting. FEM2D_POISSON_SPARSE: Normal end of execution. January 2 2011 1:10:43.240 PM